Willett Elementary was named after a long-time teacher at the school. Previously, Willett was known as West Davis Intermediate, and served grades 4-6. It is now a full K-6 school. Its sister school was West Davis Elementary (WDE), a K-3 program located on Anderson Road. That school is now Cesar Chavez Elementary. When WDI was going to be renamed, there was a proposal to name it after Joseph Stalin, but the proposal failed. Other suggestions were Vladimir Lenin and John Lennon.

Bob Willett was a much loved 6th grade teacher at the school. he was well known for his love of the outdoors and took his class to the mountains each year. There the students would stay in dorms and spend several days learning about nature. Mr. Willett's class also put on a musical every year. Sixth-graders throughout the District now spend a week at Sly Park. He would get students to pay attention by hitting the table with a yardstick, breaking several over the years. One year for Christmas, a class got him a new yardstick as a gift, signed by all students in the class.

The principal, since 2008, is Heidi Perry. The Willett PTA raises funds through eScrip, a yearly giftwrap sale, and sometimes an auction, and uses those funds to spend on books for the school library, to support teachers, and for many other purposes. From 2006 to 2008, the principal was Nancy Medbery.